Reduced order modeling of hybrid soft-rigid robots using global, local, and state-dependent strain parameterization

The need for fast and accurate analysis of soft robots calls for reduced order models (ROM). Among these, the relative reduction of strain-based ROMs follows the discretization of the strain to capture the configurations of the robot. Based on the geometrically exact variable strain parametrization of the Cosserat rod, we developed a ROM that necessitates a minimal number of degrees of freedom to represent the state of the robot: the Geometric Variable Strain (GVS) model. This model allows the static and dynamic analysis of open-, branched-, or closed-chain soft-rigid hybrid robots, all under the same mathematical framework. This paper presents for the first time the complete GVS modeling framework for a generic hybrid soft-rigid robot. Based on the Magnus expansion of the variable strain field, we developed an efficient recursive algorithm for computing the Lagrangian dynamics of the system. To discretize the soft link, we introduce state- and time-dependent basis, which is the most general form of strain basis. We classify the independent bases into global and local bases. We propose "FEM-like" local strain bases with nodal values as their generalized coordinates. Finally, using four real-world applications, we illustrate the potential of the model developed. We think that the soft robotics community will use the comprehensive framework presented in this work to analyze a wide range of specific robotic systems.